If they are paying you your rate, WTF do you care if its teaching someone or coding?
Do you honestly believe that your all that?
Get over yourself, and do your job.
Last job I quit, they called me for a year with questions. Simple shit, as long as it was less than an hour I didn't even charge them.

I cannot run my company, if I have to bargain for the invention that I paid my employee to develop.
Now that being said, if I the employee developed the invention completely separate from the company then he certainly should own it.

Apparently you don't live in New Jersey; we employ the homeless to hold signs at all the intersections, advertising all of the furniture stores doing their weekly going out of business sales. For some reason that no one understands the stores never actually go out of business, its just one of those mysteries.

I switch to Linux in 1993 because Windows was an unstable disaster. Now I am so comfortable with Linux I could never change, even if Windows became a better solution.
So if I had to be honest I would have to admit that I am a Linux guy and will never switch for the same reasons that most Windows guys would never consider Linux. Its just inside their comfort zone.

Stop with the video, stop with the blogs, stop with the pictures.
Just try to live the remaining time as full as possible. YOUR families memories of the good times is enough, make sure you have lots of them.

Your town gave them contract, they are trying to change the terms after the fact.
Inform them this is unacceptable, and will require a renegotiation in their contract.
They will cave in instantly, if they lose the contract for your town it will be a huge loss to them.
Walk down the hall and inform the council about this.